{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:SSYX3UC6GVN2PYQF2DLWQ5CMWT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d463c22c1c2982d11f5b7bfe0a0c45e0853ef122a137be0a0ab715b78d3888c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-02-23T11:24:02Z","title_canon_sha256":"8e0d34077875a1a0409c13e62f51d6a94323113ae9425aeb0705a6664d079b13"},"schema_version":"1.0","source":{"id":"2202.11433","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.11433","created_at":"2026-07-05T06:45:47Z"},{"alias_kind":"arxiv_version","alias_value":"2202.11433v2","created_at":"2026-07-05T06:45:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.11433","created_at":"2026-07-05T06:45:47Z"},{"alias_kind":"pith_short_12","alias_value":"SSYX3UC6GVN2","created_at":"2026-07-05T06:45:47Z"},{"alias_kind":"pith_short_16","alias_value":"SSYX3UC6GVN2PYQF","created_at":"2026-07-05T06:45:47Z"},{"alias_kind":"pith_short_8","alias_value":"SSYX3UC6","created_at":"2026-07-05T06:45:47Z"}],"graph_snapshots":[{"event_id":"sha256:e234059d07611e26cbf6111e0ffd3006d2b301383948db0ff20a46e72b7f5134","target":"graph","created_at":"2026-07-05T06:45:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2202.11433/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a connected algebraic group and let $X$ be a smooth projective $G$-variety. In this paper, we prove a sufficient criterion to determine the bigness of the tangent bundle $TX$ using the moment map $\\Phi_X^G:T^*X\\rightarrow \\mathfrak{g}^*$. As an application, the bigness of the tangent bundles of certain quasi-homogeneous varieties are verified, including symmetric varieties, horospherical varieties and equivariant compactifications of commutative linear algebraic groups. Finally, we study in details the Fano manifolds $X$ with Picard number $1$ which is an equivariant compactificatio","authors_text":"Jie Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-02-23T11:24:02Z","title":"On moment map and bigness of tangent bundles of $G$-varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.11433","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b73bef82bb2cebc76607a818d60be837eab6d3c4d66c3ce8e5e436c447b92575","target":"record","created_at":"2026-07-05T06:45:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d463c22c1c2982d11f5b7bfe0a0c45e0853ef122a137be0a0ab715b78d3888c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-02-23T11:24:02Z","title_canon_sha256":"8e0d34077875a1a0409c13e62f51d6a94323113ae9425aeb0705a6664d079b13"},"schema_version":"1.0","source":{"id":"2202.11433","kind":"arxiv","version":2}},"canonical_sha256":"94b17dd05e355ba7e205d0d768744cb4e3955873cbcb82adf7e91f8938bf7fc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94b17dd05e355ba7e205d0d768744cb4e3955873cbcb82adf7e91f8938bf7fc4","first_computed_at":"2026-07-05T06:45:47.343535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:45:47.343535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ndhvgwxDtp+6my541cGDry0dFqCCuah6upmK3crXpbwBOwSscDNTIKFNfNM0nZJVpF2GJyxl7PHts8F47QNMDw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:45:47.344160Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.11433","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b73bef82bb2cebc76607a818d60be837eab6d3c4d66c3ce8e5e436c447b92575","sha256:e234059d07611e26cbf6111e0ffd3006d2b301383948db0ff20a46e72b7f5134"],"state_sha256":"2f042517d1ea97579fe48aa8528c6746b02bb73d4c801ca63834a7e161297c0b"}